Brahmagupta matrix - Alchetron, The Free Social Encyclopedia

In mathematics, the following matrix was given by Indian mathematician Brahmagupta:

B ( x , y ) = [ x y ± t y ± x ] .

It satisfies

B ( x 1 , y 1 ) B ( x 2 , y 2 ) = B ( x 1 x 2 ± t y 1 y 2 , x 1 y 2 ± y 1 x 2 ) .

Powers of the matrix are defined by

B n = [ x y t y x ] n = [ x n y n t y n x n ] ≡ B n .

The x n and y n are called Brahmagupta polynomials. The Brahmagupta matrices can be extended to negative integers:

B − n = [ x y t y x ] − n = [ x − n y − n t y − n x − n ] ≡ B − n .

References

(Text) CC BY-SA